Pretty much ALL of the danger themes in this video.
Especially the death themes, combined with the message that appears. "Deepest sympathy! Sim has just died. Though body is gone, spirit will always remain".
The sting (heard in the beginning of the video above) played when the burglar (or some other dangerous event, such as raccoons and getting fired) appears on your lot in the first game. The combination of the eerie music, the picture in the corner highlighting the burglar's furtive and ever-forward movements, and the knowledge that you can't do anything about it - not even cheating! - save for calling the police, is simply terrifying. Oh, and sometimes it happens that a burglar appears in the lot, but leaves immediately afterwards. Let's not forget that this usually happens late at night (typically during the hour after midnight), when all of your Sims are asleep and everything is quiet except for the chirping crickets - you couldn't be in a more tender, vulnerable state of mind when danger suddenly strikes. The burglar music scarred so many childhoods that all future Sims games would water down the accompanying theme considerably.
The Fire 2 sting is reminiscent of "Psycho" Strings, and it shows. You will no longer want to leave your Sims with the Cooking skill below 3, or put in chimneys, or use the firework kits, lest you will hear that terrifying theme again... not that Fire 1 is not scary, but at least it lacks the strings.
The music when ghosts appear on the lot (also heard in the same video). The wailing and laughing noises they make when floating around don't exactly help.
Even if they're meant to be prank calls, a lot of the messages your Sims hear when answering a ringing phone are downright creepy. Special mention goes to "They're coming soon. Better think twice about opening the door." And while you read the message, the little mask in the dialogue box just stares at you. Smiling. Here is a list of all the prank call messages; they run the gamut from mundane ("Wrong number. Sorry.") to innocuously bizarre and silly ("Do you canoe?") to vaguely unsettling ("The drop off has been made. You've been warned.") to FUCKING OMINOUS ("The end is near. Make preparations.").
"The flashing light was just a test. You'll have plenty of warning next time."
"You have been Chosen. They will come soon."
One lot in Magic Town, "Coldwind Meadow", has a fairly unsettling description:
Once a dairy pasture, this quiet meadow was usually avoided by local farmers following the unexplained disappearance of their cows. Recently, a carnival blew into town and set up several unusual attractions on this mysterious site.
The dying screams of your Sims are much, MUCH more pained and horrifying than in future games.
Unleashed introduced a glitch in which sometimes a Sim's portrait image would be corrupted and inaccessible. The game tries to compensate for that issue by showing a pointy-eared woman's head upside-down◊ instead. It stands out so much players are easily startled when this portrait appears out of nowhere... not to mention that this portrait emotes unlike the default ones. Oh, and it can spread to other Sims and there's no fix apart from manually editing the affected Sim.
In The Sims: Livin Large, there was something called Concoctonation Station. Sims can make various potions, but can be fined if caught by police. Some potions make the Sims mood better, but others can change the Sims personality or make their mood low, including hunger, putting them at risk for imminent starvation. Others make Sims fall in love or turn invisible for a time. Two negative effect potions make a temporary evil clone of a Sim or turns a Sim into a Frankensteins monster-like thing. Their mood tanks dramatically and they cant be controlled. All they do is walk around and break things while making a strange roaring noise, and they wake up sleeping Sims upon entering a room. They change back eventually, but its still unnerving. Its impossible to control which potion is made, so its a gamble each time.
The Sims 2
It is unknown whether the alien babies come from intercourse or artificial insemination, but the only difference is the kind of trauma the Sim should have from that, especially after ending up with a green-skinned, black-eyed child that looks just like the aliens abusing you. Yes, the Mr. Seahorse-scene is funny, but would you (assuming you're not a Knowledge Sim) want to be the one who it happened to? It makes GeneralBuzz Grunt's hatred of aliens a bit justified.
The ghosts. Especially the red ones. Worse, the fact that the ghosts can literally scare your Sims to death.
The Ottomas Twins had missing genetic data from their father's side when they were initially added into the game. That means the game has to improvise and set someone else as the father - which can be anything from a random male Sim, random female Sims, NPCs such as the Grim Reaper, or even pets. Due to this, they can have disturbingly hideous and deformed faces. They've been known even to corrupt the game. Not that their siblings and grandmother are lookers either.
The hula zombie music. It IS a death theme, but it's still surprising how eerily spooky and depressing it is.
If you zoom in so much that the camera clips through a Sim's head, you can see a part of their skin texture in their teeth. It's worse than it sounds.◊
A Sim with extremely low hygiene in a room with many fly-infested dirty objects risk being Eaten Alive by a swarm of hungry flies. Oh, and the Sim will have enough time to scream before turning into a pile of dust. It's easily the most horrifying death, but it's thankfully extremely hard to trigger in normal gameplay.
With a bit of work, you can set up an And I Must Scream situation using the Cowplant and the Resurrect-O-Nomitron. Repeatedly feed the Cowplant with a Sim and then have another Sim drink the Cowplant's milk, thereby extending their own life. Then call the Grim Reaper and cough up the money to resurrect the dead Sim and feed him/her again to the Cowplant, rinse and repeat for eternal life as long as you have enough money to pay the Grim Reaper, and the poor Sim will be stuck in a constant state of being Eaten Alive and then resurrected until the one resurrecting him/her stops. Fun!
The existence of zombies. While the Zombie Apocalypse is utterly averted and zombies aren't dangerous in game, it's heavily implied that the zombified Sim resents their resurrection as it robs them of their eternal rest (they get a bad memory and lose relationship with the one who resurrected them). Oh, and it's also permanent, once a Sim becomes a zombie, they will stay like that forever... And we do mean forever, they're biologically immortal. Their personality is also wiped out and they all have a new fixed one with 4 Outgoing, 3 Active and 1 Playful point and they lose all their skills. It almost feel like a Mercy Kill when they die and are never resurrected again.
Signs of neighborhood corruption. If you delete a Sim (or the tombstone of a Sim) who had met with someone else at one point, or try to resurrect a Sim whose data is incomplete, the neighborhood will slowly get crazy. The Sims that interacted with that one Sim that was deleted would occasionally think of glitch memories◊ where, instead of the deleted Sim's portrait, you'd have random icons from the game. This would be rather tame except for the fact that Sims speak to each other, something that makes the glitched memories start spreading like a virus, ending with a whole neighborhood of crazy people that talk about a Sim that does not exist, Sims disappearing from the game, Sims that are Younger or Older Than They Look (which can end up with things like floating children), Children with an Aspiration other than Grow Up and impossible wishes such as Children wanting to go on a date, or Sims wanting to be friends with themselves. The corruption keeps going up to the point where the game simply fails load the horribly-corrupted neighborhood.
A few of the spells introduced in Apartment Life have some very disturbing implications.
Any time an NPC brings their toddler to the library, the kid crawls over to the toychest and literally disappears into the box. And if you teleport home when holding the neighbour's infant (uh, kidnapping), there's a good chance the infant will turn into an invisible, unfindable, crying baby!
World Adventures: The death by Mummy's Curse. A very unlikely death, given how it occurs, but it's pretty unsettling all the same. For starters, when your Sim loses the fight with the Mummy, the Mummy has a chance of casting some kind of spell on them, with them screaming all the while. And a few days in, a strange border begins appearing around the screen when the view is on the Sim in question. When theres only a few hours left, the game feels the need to add a Scare Chord to emphasise the impending demise of the Sim, after which the aforementioned border gets accompanied by a skull fading in and out of view, which gets more and more intense the longer the Curse is left. Eeesh. And then, when the time of death finally comes, the Sim is surrounded by a tornado and... just blows away. It's a very creepy death, especially in comparison to the rest of the deaths.
The Mysterious Mr. Gnome and his variations. It's this weird-looking gnome with Offscreen Teleportation abilities, and it can appear by your Sim's bed to watch them sleep. And there's nothing you can do to contain it. Seanbaby doesn't appear to be aware of this particular feature - when he does a brief Let's Play of the game as an experiment in "psychology", several of the gnomes he set up to stare at the toilet so his subject would never feel comfortable peeing relocate to surrounding guard positions during the solitary confinement portion of the experiment. When he notices this, he expresses doubts about his own sanity (the sanity of his subject isn't exactly in question - it's quite definitively not there).
The Werewolf transformation. The Sim looks (and sounds) like they're in pain when it happens. And if you're playing with the game on full moon, it happens whether you like it or not!
Sims with the Supernatural Skeptic trait has special social interactions. Some are funny enough, like "imply mother is a junebug" when talking to fairies, but some are... unsettling. For example: Look through the options and see "Enthuse about Witch Hunts". The speech bubble even depicts three torches. Keep in mind that witch executions are usually depicted as them being being burned at the stake.
Some of the new paintings for this expansion changes their appearance at night... and all of their alternative looks are visions of hell, death, or evil.
In the haunted house (the attraction, not a literal haunted house), look closely at the windows. This may sound stupid at first, but the person who dresses up as a ghost (by donning a bedsheet...) actually looks surprisingly creepy as it strides back and forth from window to window. It's the fluid movement that sells it.
If you forget to pay your bills for some time, a repo-sim will be sent to your house to reclaim some of your stuff (equivalent to the amount of money you owe). Unfortunately, the game gives no notification or warning whatsoever, and when it happens, a fairly ominous piece of music plays and suddenly a shady-looking sim in dark gray clothing enters your house and starts taking stuff. Many first-time players mistake the repo-sim for a burglar. Not exactly nightmarish, but still fairly alarming.
The Kraken that comes with "Island Paradise". Especially because it will often swim under your houseboat. Also, sharks.
The "glitched baby" problem, which can happen if you accidentally download corrupted custom content. Nothing quite like having your newborn baby look like a featureless flesh-colored stick or a giant blob which eventually grows up into a horrid, deformed, shapeless Lovecraftian mess. You want to know something worse? Said corrupted content can attach to other things on The Exchange, so even if someone tries to avoid using it, that content could still sneak into their uploads. To make THAT worse, this is how computer viruses spread, so these glitched babies are a sign of a very specific virus.
Pets can have the glitched baby problem sometimes too (but no corrupted downloaded content is necessary). It's uncertain what causes it but while speeding up time in the PS3 Sims Pets sometimes dogs or cats will suddenly shoot up onto two legs with the distorted glitch form.
In-universe example. Checking for monsters under the bed. If you find nothing, fine. If you see glowing eyes, the kid will refuse to sleep in that bed for an entire night.
An in-game example. When Toddlers and Children play with an evil clown-in-a-box, they get scared to the point that it's recorded as a bad memory. Mean (grouchy) Sims apparently do not get a bad memory when playing with the evil clown-in-a-box, but enjoy it instead.
Meteors. Overlapping with Paranoia Fuel, these things can fall and kill your Sim if you have Ambitions installed at literally any time you're outside. While there is a pretty big warning to get out of the way, and a meteor has to get a direct hit, it is more than possible to go AFK without pausing only to find your camera zoomed in on a smouldering, 3x2 hunk of rock when you return.
If the game is paused at just the right time, some of the Sims' faces can look downright spooky. On that note, pausing the game does not always immediately stop a Sim's animations, often allowing them to complete a tiny movement such as a few frames of a head turn or the like. It's subtle enough that most people won't notice it until they either look for it, or their Sim appears to turn their head towards the screen.
The Sims 4
Children can't burn, but they can drown. You can end up with child ghosts.
You can romance the Grim Reaper, flirting with him whenever he comes to harvest souls. But he only calls when somebody dies, so to romance him, you have to kill more Sims!
Vampire attacks at night. An ominous music sting will play as the vampire enters your Sim's house and does a Nosferatu-style walk to their bedroom, all with you powerless to do anything about it. If your Sim gets drained by Vlad, you may also get a message in which he declares his intentions to return and feed again whenever he wants, since your Sim's plasma is just that delicious.
The StrangerVille pack has, in a short time, become infamous for supplying a deep well of this, in a series not normally known for having overtly, deliberately scary content other than Defanged Horrors or Video Game Cruelty Potential.
For starters, it introduces a very frightening new feature: possessed sims. Once possessed, they will have an unnatural, wide smile on their faces, coupled with large, staring eyes. Their walk will be janky and twitchy, and they will run in a inhumane manner, very similarly to how The Smiling Man moves. If a non-possessed sim tries to communicate with them, they will say very creepy things back, with all of their dialogue written in a strange font to reflect the fact that something's wrong with them. The worst part is how they look in their emotion stature; unlike all other emotion postures wherein the sims stare off in front of them, the possessed sim will look directly at you. To say this alienated and scared some players the first time they saw it would be an understatement. Furthermore, if you play in StrangerVille, these guys will be your first guests, with the "Welcome Wagon" event replaced by a "Welcome to StrangerVille" event where, instead of your new neighbors greeting you, it's a whole bunch of possessed sims showing up at your front door. (One of them is even holding the customary fruitcake, as the cherry on top.)
It only continues once you start digging into the StrangerVille mystery. Once you complete part two and open the locked door in the secret lab, you accidentally release a whole bunch of spores all over town. The sky turns a strange, reddish color, with purple spores floating in the air and a plume of smoke coming from the direction of the lab. Combine that with the fact that the strange, glowing plants found around StrangerVille have just expanded in both size and number (including vines that now come out of your plumbing), the preexisting knowledge that something in StrangerVille is causing sims to act possessed, and that traveling deeper into the secret lab's lower levels requires a Hazmat Suit... it doesn't take much for a player to connect the dots and realize that they probably just exposed their sims, and everyone else in town, to whatever infection is responsible for the possession.
A bit mild, but when the Gotta Stream 'Em All drone breaks down, it billows smoke, spinning midair in a circle and starts screaming. Definitely catches you off guard the first time it happens. And second. And third...